Rewrite ((5^5)(8^-5))^10 in the form 5^m *8^n
$$\\((5^5)(8^{-5}))^{10} \\\\ =(5^5*8^{-5})^{10} \\\\ =5^{5*10}*8^{-5*10} \\\\ =5^{50}*8^{-50} \\\\$$